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60 PHYSICS since we are talking of uncharged and non- exist by itself. When there is no applied force, magneticbodiesinmechanics.Atthemicroscopic there is no static friction. It comes into play the level, all bodies are made of charged constituents moment there is an applied force. As the applied (nuclei and electrons) and the various contact force F increases, f slso increases, remaining equal and opposite to the applied force (up to a forcesarisingduetoelasticityofbodies,molecular certain limit), keeping the body at rest. Hence, it collisions and impacts, etc. can ultimately be tracedtotheelectricalforcesbetweenthecharged is called static friction. Static friction opposes constituents of different bodies. The detailed impending motion. The term impending motion means motion that would take place (but does microscopic origin of these forces is, however, not actually take place) under the applied force, complex and not usefulforhandling problems in mechanics at the macroscopic scale. This is why if friction were absent. they are treated as different types of forces with We know from experience that as the applied force exceeds a certain limit, the body begins to their characteristic properties determined move. It is found experimentally that the limiting empirically. value of static friction( s is independent of max 4.9.1 Friction the area of contact and varies with the normal Let us return to the example of a body of mass m force(N) approximately as : at rest on a horizontal table. The force of gravity ( s = µsN (4.13) (mg) is cancelled by the normal reaction force max (N) of the table. Now suppose a force F is applied where µs is a constant of proportionality depending only on the nature of the surfaces in horizontally to the body. We know from contact. The constant µ is called the coefficient experience that a small applied force may not of static friction. The law of static friction may be enough to move the body. But if the applied force F were the only external force on the body, thus be written as fs≤ µ sN (4.14) it must move with acceleration F/m, however small. Clearly, the body remains at rest because If the applied force F exceeds ( s max the body some other force comes into play in the begins to slide on the surface. It is found experi- horizontal direction and opposes the applied mentally that when relative motion has started, force F, resulting in zero net force on the body. the frictional force decreases from the static This force fsparallel to the surface of the body in contact with the table is known as frictional maximum value ( s max. Frictional force that opposes relative motion between surfaces in force, or simply friction (Fig. 4.10(a)). The contact is called kinetic or sliding friction and is subscript stands for static friction to distinguish it from kinetic friction f that we consider later denoted by f .kKinetic friction, like static fric- (Fig. 4.10(b)). Note that static friction does not tion, is found to be independent of the area of contact. Further, it is nearly independent of the velocity. It satisfies a law similar to that for static friction: f = µ N (4.15) k k where µ k′the coefficient of kinetic friction, depends only on the surfaces in contact. As mentioned above, experiments show that µ is k Fig. 4.10 Static and sliding friction: (a) Impending less than µs. When relative motion has begun, motion of the body is opposed by static the acceleration of the body according to the friction. When external force exceeds the second law is ( F – k )/m. For a body moving with maximum limit of static friction, the body constant velocity, F = f k If the applied force on begins to move. (b) Once the body is in the body is removed, its acceleration is – f /m motion,itissubjecttoslidingorkineticfrictionand it eventually comes to a stop. k which opposes relative motion between the The laws of friction given above do not have two surfaces in contact. Kinetic friction isthe status of fundamental laws like those for usuallylessthanthemaximumvalueofstatic gravitational, electric and magnetic forces. They friction. are empirical relations that are only Reprint 2026-27